# Thread: Formula for calculating height displacement of a scissor jack

1. ## Formula for calculating height displacement of a scissor jack

Hi,

I am trying to design a scissor jack for a little project I am working on.

Can anyone point me in the direction of a formula that I can use to calculate the height displacement of the jack, given the specs on the threaded rod and lengths of the arms used?

Namely I am intersted in determing the hight dieplacement per revolution of the threaded rod.

Also, what about lateral forces, i.e. forces against the sides of the jack, instead of forces in the direction of travel? In other words, what is the best type of design configuration, or what steps can be taken, that would minimize or resist side to side movement once the jack is extended?

Thanks.

2. Originally Posted by nadsab
Hi,

I am trying to design a scissor jack for a little project I am working on.

Can anyone point me in the direction of a formula that I can use to calculate the height displacement of the jack, given the specs on the threaded rod and lengths of the arms used?

Namely I am intersted in determing the hight dieplacement per revolution of the threaded rod.

Thanks.
It’s hard to write formulas here but think about just one side of the scissors and remember that if z is length of scissors and x and y are the base and height of the triangle described by the scissors link then z^2=x^2 +y^2, where z^2 reads ‘z squared’. x=z-P*R where P is pitch of lead screw and R is the number of revolutions of the crank, 1.5 means one and a half full turns. The z-PR term implies that R=0 is where the scissors link is horizontal. Then the formula you want is

Y^2=z^2-(z-PR)^2 or y=SquareRootOf(z^2-(z-PR)^2 ). If the scissors jack has multiple links (N) then this formula gives the lift from each link so multiply it by N to get the total displacement.

To answer the questions in the other post that is not a linear equation for displacement. Alternatives to scissors jacks include (a) wedges and cams, (b) screws, (c) inflatables like air bags or hydraulic cylinders. The link part of a scissors jack can be employed in a number of ways that seem different that a scissors jack but all use the same type equation for displacement so all are functionally equivalent.

Tom

3. Thanks very much TomB for the formulas.

So to sum up, would it be possible to devise in some way a non linear adjustment screw, and what I mean by non linear, is there a method available to having a simple type of adjustment wheel on the lead screw, which would indicate the non linear displacement of the jack? Other than using some kind of a seperate dial gauge to measure the displacement?

4. Hi, you could use one of those short Z axis digital indicators they make for the quill travel on the Bridgeport type mill, to show the actual travel of the scissor jack.

Try Ebay for a supplier.

The scale is similar to a 150mm digital caliper gauge, and is about 300 mm long with a larger read out available if'n you want to view the read out away from the machine.

With this method you will get an exact indication (to 2 dec places mm, 3 Imperial), of the jack's lift movement as opposed to trying to calibrate the drive screw.
Ian.